LEADER 01095nam0-22003011i-450- 001 990002901910403321 005 20080527102503.0 035 $a000290191 035 $aFED01000290191 035 $a(Aleph)000290191FED01 035 $a000290191 100 $a20030910d1999----km-y0itay50------ba 101 0 $aita 102 $aIT 200 1 $aAtti della 39. riunione scientifica$e[della SIS], Sorrento 14-17 aprile 1998$esessioni plenarie, sessioni specializzate$fIstituto di Statistica e Matematica [dell']Istituto Universitario Navale di Napoli 210 $aNapoli$cIstituto di statistica e matematica. Istituto universitario navale di Napoli$d1999 215 $a360 p.$d24 cm$ecd-rom 610 0 $aSocietà Italiana di Statistica 610 0 $aSocietà Italiana di Statistica$aRiunioni scientifiche 676 $a001.4 710 02$aSocietà italiana di statistica$0102283 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990002901910403321 952 $aXXXI-A-59$b7064$fMAS 959 $aMAS 996 $aAtti della 39. riunione scientifica$9466394 997 $aUNINA LEADER 06444oam 2200541 450 001 9910830347203321 005 20230118005908.0 010 $a1-119-98858-6 010 $a1-119-98856-X 035 $a(MiAaPQ)EBC7018990 035 $a(Au-PeEL)EBL7018990 035 $a(CKB)23899484800041 035 $aEBL7018990 035 $a(AU-PeEL)EBL7018990 035 $a(OCoLC)1331704791 035 $a(OCoLC-P)1331704791 035 $a(CaSebORM)9781786308276 035 $a(EXLCZ)9923899484800041 100 $a20221222h20222022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntegrable systems /$fAhmed Lesfari 210 1$aHoboken, New Jersey :$cJohn Wiley & Sons, Incorporated,$d2022. 210 4$d©2022 215 $a1 online resource (332 pages) 300 $aDescription based upon print version of record. 311 08$aPrint version: Lesfari, Ahmed Integrable Systems Newark : John Wiley & Sons, Incorporated,c2022 9781786308276 320 $aIncludes bibliographic references and index. 327 $aCover -- Half-Title Page -- Dedication -- Title Page -- Copyright Page -- Contents -- Preface -- Chapter 1. Symplectic Manifolds -- 1.1. Introduction -- 1.2. Symplectic vector spaces -- 1.3. Symplectic manifolds -- 1.4. Vectors fields and flows -- 1.5. The Darboux theorem -- 1.6. Poisson brackets and Hamiltonian systems -- 1.7. Examples -- 1.8. Coadjoint orbits and their symplectic structures -- 1.9. Application to the group SO(n) -- 1.9.1. Application to the group SO(3) -- 1.9.2. Application to the group SO(4) -- 1.10. Exercises -- Chapter 2. Hamilton-Jacobi Theory -- 2.1. Euler-Lagrange equation -- 2.2. Legendre transformation -- 2.3. Hamilton's canonical equations -- 2.4. Canonical transformations -- 2.5. Hamilton-Jacobi equation -- 2.6. Applications -- 2.6.1. Harmonic oscillator -- 2.6.2. The Kepler problem -- 2.6.3. Simple pendulum -- 2.7. Exercises -- Chapter 3. Integrable Systems -- 3.1. Hamiltonian systems and Arnold-Liouville theorem -- 3.2. Rotation of a rigid body about a fixed point -- 3.2.1. The Euler problem of a rigid body -- 3.2.2. The Lagrange top -- 3.2.3. The Kowalewski spinning top -- 3.2.4. Special cases -- 3.3. Motion of a solid through ideal fluid -- 3.3.1. Clebsch's case -- 3.3.2. Lyapunov-Steklov's case -- 3.4. Yang-Mills field with gauge group SU(2) -- 3.5. Appendix (geodesic flow and Euler-Arnold equations) -- 3.6. Exercises -- Chapter 4. Spectral Methods for Solving Integrable Systems -- 4.1. Lax equations and spectral curves -- 4.2. Integrable systems and Kac-Moody Lie algebras -- 4.3. Geodesic flow on SO(n) -- 4.4. The Euler problem of a rigid body -- 4.5. The Manakov geodesic flow on the group SO(4) -- 4.6. Jacobi geodesic flow on an ellipsoid and Neumann problem -- 4.7. The Lagrange top -- 4.8. Quartic potential, Garnier system -- 4.9. The coupled nonlinear Schrödinger equations -- 4.10. The Yang-Mills equations. 327 $a4.11. The Kowalewski top -- 4.12. The Goryachev-Chaplygin top -- 4.13. Periodic infinite band matrix -- 4.14. Exercises -- Chapter 5. The Spectrum of Jacobi Matrices and Algebraic Curves -- 5.1. Jacobi matrices and algebraic curves -- 5.2. Difference operators -- 5.3. Continued fraction, orthogonal polynomials and Abelian integrals -- 5.4. Exercises -- Chapter 6. Griffiths Linearization Flows on Jacobians -- 6.1. Spectral curves -- 6.2. Cohomological deformation theory -- 6.3. Mittag-Leffler problem -- 6.4. Linearizing flows -- 6.5. The Toda lattice -- 6.6. The Lagrange top -- 6.7. Nahm's equations -- 6.8. The n-dimensional rigid body -- 6.9. Exercises -- Chapter 7. Algebraically Integrable Systems -- 7.1. Meromorphic solutions -- 7.2. Algebraic complete integrability -- 7.3. The Liouville-Arnold-Adler-van Moerbeke theorem -- 7.4. The Euler problem of a rigid body -- 7.5. The Kowalewski top -- 7.6. The Hénon-Heiles system -- 7.7. The Manakov geodesic flow on the group SO(4) -- 7.8. Geodesic flow on SO(4) with a quartic invariant -- 7.9. The geodesic flow on SO(n) for a left invariant metric -- 7.10. The periodic five-particle Kac-van Moerbeke lattice -- 7.11. Generalized periodic Toda systems -- 7.12. The Gross-Neveu system -- 7.13. The Kolossof potential -- 7.14. Exercises -- Chapter 8. Generalized Algebraic Completely Integrable Systems -- 8.1. Generalities -- 8.2. The RDG potential and a five-dimensional system -- 8.3. The Hénon-Heiles problem and a five-dimensional system -- 8.4. The Goryachev-Chaplygin top and a seven-dimensional system -- 8.5. The Lagrange top -- 8.6. Exercises -- Chapter 9. The Korteweg-de Vries Equation -- 9.1. Historical aspects and introduction -- 9.2. Stationary Schrödinger and integral Gelfand-Levitan equations -- 9.3. The inverse scattering method -- 9.4. Exercises. 327 $aChapter 10. KP-KdV Hierarchy and Pseudo-differential Operators -- 10.1. Pseudo-differential operators and symplectic structures -- 10.2. KdV equation, Heisenberg and Virasoro algebras -- 10.3. KP hierarchy and vertex operators -- 10.4. Exercises -- References -- Index -- Other titles from iSTE in Mathematics and Statistics -- EULA. 330 $aThis book illustrates the powerful interplay between topological, algebraic and complex analytical methods, within the field of integrable systems, by addressing several theoretical and practical aspects. Contemporary integrability results, discovered in the last few decades, are used within different areas of mathematics and physics. Integrable Systems incorporates numerous concrete examples and exercises, and covers a wealth of essential material, using a concise yet instructive approach. This book is intended for a broad audience, ranging from mathematicians and physicists to students pursuing graduate, Masters or further degrees in mathematics and mathematical physics. It also serves as an excellent guide to more advanced and detailed reading in this fundamental area of both classical and contemporary mathematics. 606 $aIntegral equations 606 $aHamiltonian systems 615 0$aIntegral equations. 615 0$aHamiltonian systems. 676 $a658.4034 700 $aLesfari$b Ahmed$01701041 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830347203321 996 $aIntegrable systems$94084515 997 $aUNINA LEADER 07299nam 22007815 450 001 9910970542603321 005 20250801082546.0 010 $a3-642-61068-4 024 7 $a10.1007/978-3-642-61068-4 035 $a(CKB)1000000000016918 035 $a(SSID)ssj0000914835 035 $a(PQKBManifestationID)11466078 035 $a(PQKBTitleCode)TC0000914835 035 $a(PQKBWorkID)10866320 035 $a(PQKB)11329529 035 $a(DE-He213)978-3-642-61068-4 035 $a(MiAaPQ)EBC3093727 035 $a(EXLCZ)991000000000016918 100 $a20110907d1996 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aNeural Networks $eA Systematic Introduction /$fby Raul Rojas 205 $a1st ed. 1996. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1996. 215 $a1 online resource (XX, 502 p. 154 illus.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-60505-3 320 $aIncludes bibliographical references and index. 327 $a1. The Biological Paradigm -- 1.1 Neural computation -- 1.2 Networks of neurons -- 1.3 Artificial neural networks -- 1.4 Historical and bibliographical remarks -- 2. Threshold Logic -- 2.1 Networks of functions -- 2.2 Synthesis of Boolean functions -- 2.3 Equivalent networks -- 2.4 Recurrent networks -- 2.5 Harmonic analysis of logical functions -- 2.6 Historical and bibliographical remarks -- 3.Weighted Networks ? The Perceptron -- 3.1 Perceptrons and parallel processing -- 3.2 Implementation of logical functions -- 3.3 Linearly separable functions -- 3.4 Applications and biological analogy -- 3.5 Historical and bibliographical remarks -- 4. Perceptron Learning -- 4.1 Learning algorithms for neural networks -- 4.2 Algorithmic learning -- 4.3 Linear programming -- 4.4 Historical and bibliographical remarks -- 5. Unsupervised Learning and Clustering Algorithms -- 5.1 Competitive learning -- 5.2 Convergence analysis -- 5.3 Principal component analysis -- 5.4 Some applications -- 5.5 Historical and bibliographical remarks -- 6. One and Two Layered Networks -- 6.1 Structure and geometric visualization -- 6.2 Counting regions in input and weight space -- 6.3 Regions for two layered networks -- 6.4 Historical and bibliographical remarks -- 7. The Backpropagation Algorithm -- 7.1 Learning as gradient descent -- 7.2 General feed-forward networks -- 7.3 The case of layered networks -- 7.4 Recurrent networks -- 7.5 Historical and bibliographical remarks -- 8. Fast Learning Algorithms -- 8.1 Introduction ? classical backpropagation -- 8.2 Some simple improvements to backpropagation -- 8.3 Adaptive step algorithms -- 8.4 Second-order algorithms -- 8.5 Relaxation methods -- 8.6 Historical and bibliographical remarks -- 9. Statistics and Neural Networks -- 9.1 Linear and nonlinear regression -- 9.2 Multiple regression -- 9.3Classification networks -- 9.4 Historical and bibliographical remarks -- 10. The Complexity of Learning -- 10.1 Network functions -- 10.2 Function approximation -- 10.3 Complexity of learning problems -- 10.4 Historical and bibliographical remarks -- 11. Fuzzy Logic -- 11.1 Fuzzy sets and fuzzy logic -- 11.2 Fuzzy inferences -- 11.3 Control with fuzzy logic -- 11.4 Historical and bibliographical remarks -- 12. Associative Networks -- 12.1 Associative pattern recognition -- 12.2 Associative learning -- 12.3 The capacity problem -- 12.4 The pseudoinverse -- 12.5 Historical and bibliographical remarks -- 13. The Hopfield Model -- 13.1 Synchronous and asynchronous networks -- 13.2 Definition of Hopfield networks -- 13.3 Converge to stable states -- 13.4 Equivalence of Hopfield and perceptron learning -- 13.5 Parallel combinatorics -- 13.6 Implementation of Hopfield networks -- 13.7 Historical and bibliographical remarks -- 14. Stochastic Networks -- 14.1 Variations of the Hopfield model -- 14.2 Stochastic systems -- 14.3 Learning algorithms and applications -- 14.4 Historical and bibliographical remarks -- 15. Kohonen Networks -- 15.1 Self-organization -- 15.2 Kohonen?s model -- 15.3 Analysis of convergence -- 15.4 Applications -- 15.5 Historical and bibliographical remarks -- 16. Modular Neural Networks -- 16.1 Constructive algorithms for modular networks -- 16.2 Hybrid networks -- 16.3 Historical and bibliographical remarks -- 17. Genetic Algorithms -- 17.1 Coding and operators -- 17.2 Properties of genetic algorithms -- 17.3 Neural networks and genetic algorithms -- 17.4 Historical and bibliographical remarks -- 18. Hardware for Neural Networks -- 18.1 Taxonomy of neural hardware -- 18.2 Analog neural networks -- 18.3 Digital networks -- 18.4 Innovative computer architectures -- 18.5 Historical and bibliographicalremarks. 330 $aArtificial neural networks are an alternative computational paradigm with roots in neurobiology which has attracted increasing interest in recent years. This book is a comprehensive introduction to the topic that stresses the systematic development of the underlying theory. Starting from simple threshold elements, more advanced topics are introduced, such as multilayer networks, efficient learning methods, recurrent networks, and self-organization. The various branches of neural network theory are interrelated closely and quite often unexpectedly, so the chapters treat the underlying connection between neural models and offer a unified view of the current state of research in the field. The book has been written for anyone interested in understanding artificial neural networks or in learning more about them. The only mathematical tools needed are those learned during the first two years at university. The text contains more than 300 figures to stimulate the intuition of the reader and to illustrate the kinds of computation performed by neural networks. Material from the book has been used successfully for courses in Germany, Austria and the United States. 606 $aArtificial intelligence 606 $aComputer simulation 606 $aPattern recognition systems 606 $aMicroprocessors 606 $aComputer architecture 606 $aComputer science 606 $aBioinformatics 606 $aArtificial Intelligence 606 $aComputer Modelling 606 $aAutomated Pattern Recognition 606 $aProcessor Architectures 606 $aTheory of Computation 606 $aComputational and Systems Biology 615 0$aArtificial intelligence. 615 0$aComputer simulation. 615 0$aPattern recognition systems. 615 0$aMicroprocessors. 615 0$aComputer architecture. 615 0$aComputer science. 615 0$aBioinformatics. 615 14$aArtificial Intelligence. 615 24$aComputer Modelling. 615 24$aAutomated Pattern Recognition. 615 24$aProcessor Architectures. 615 24$aTheory of Computation. 615 24$aComputational and Systems Biology. 676 $a006.3 700 $aRojas$b Raul$4aut$4http://id.loc.gov/vocabulary/relators/aut$061314 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910970542603321 996 $aNeural Networks$9375174 997 $aUNINA